The present invention relates to a method for determining the line segments, circular arcs and clothoidal arcs that form a complex curve. More particularly, the present invention relates to use of the ψ-s curve to identify the line segments, circular arcs and clothoidal arcs that define the shapes of roads.
Geographic databases have many uses. Geographic databases are used in navigation systems to display maps and provide route calculation and guidance. Geographic databases are also used by Internet sites to provide navigation-related features and services. Geographic databases are also used by advanced driver safety systems, such as adaptive headlight aiming, adaptive cruise control, and so on.
In many conventional geographic databases, a linearly extending geographic feature, such as a road, a river, or a state or municipal boundary, is represented using a series of discrete points. For example, in the case of roads, each road segment is represented by two nodes that represent the end points of the road segment, and optionally by one or more shape points that represent points along the road segment between the two nodes. Data that define each of these points (e.g., latitude, longitude, and optionally altitude) are stored in the geographic database to represent the road segment.
Although this way of representing roads and other linearly extending geographic features works well for many applications, there are other ways to represent the shapes of roads. In some parts of the world (including the United States), roads are designed to have shapes that are line segments and circular arcs connected end to end in various combinations. In some instances, clothoidal arcs are also used as transition curves to provide a continuously varying curvature segment that can join straight line segments and circular arcs, or different circular arc segments with continuity of curvature maintained at the join points. Therefore, one way to define the shape of a road is in terms of a series of connected straight line segments, circular arcs and clothoidal arcs.
If a road is to be represented as a series of connected line segments, circular arcs and clothoidal arcs, a means is needed to determine the locations at which each arc and straight line begins and ends, as well as the characterizing parameters of each primitive shape.
In addition to obtaining an accurate and space efficient representation of road geometry, it is also important for many applications to obtain accurate values of point radius of curvature of roads. Prior attempts at computing curvature of road geometry have been based on fitting a polynomial function to the shape points or by using an approximation to curvature such as the three-point method. These methods may be relatively complex and therefore relatively computationally intensive.
Accordingly, there is a need for an efficient way to determine the line segments, circular arcs and clothoidal arcs that form the shapes of roads.